No, definitely not. Paul had indicate three heavens - which God's throne is in the third heaven.
In Revelation 12:7-9, it doesn't say 1st, 2nd, 3rd heaven directly in the text. But it implied the second heaven, the cosmos, because Satan is cast down to earth, which our atmosphere is the first heaven. And the cosmos later in the seven years gets rolled back, in Revelation 6, the sixth seal events.
More than one level of heaven, is also in Revelation 12:
12 Therefore rejoice,
ye heavens, and ye that dwell in them. Woe to the inhabiters of the earth and of the sea! for the devil is come down unto you, having great wrath, because he knoweth that he hath but a short time.
The good angels can travel back and forth in all three heavens.